Linear algebra

Linear algebra is a branch of mathematics that concerns linear equations, vector spaces, linear maps between vector spaces, and matrices.[1]

The two planes are subsets of the 3-dimensional space, and their intersection is a line.
This affine plane is generated by two vectors and and consists of all linear combinations

We have two featured projects, both outside the namespace of this resource.

  • Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I is a mathematical course for beginners at the University of Osnabrück. It covers logical foundation, sets, mappings, algebraic structures like fields and polynomials, the basics of analysis like sequences, continuity, differentiability, primitive functions and the basics of linear algebra like vector spaces, bases, linear maps, eigenvalues. While course has been taught many times, this is a textbook -- not an online course.
Contents • Linear systems• Matrices and vector spaces• Bases and dimension• Linear mappings• Invertible matrices• Determinants• Eigenspaces• Diagonalizability

Ricci calculus is hard to learn, but it will bend your mind!
  • Tensors employs the "unorthodox" approach of using the covariant and contravariant forms associated with Ricci calculus. But keep in mind that this approach is vastly superior. It is required for General Relativity, and is the most powerful way to do vectors and tensors.
Contents: • Tensors/Definitions • Tensors/Bases • Tensors/Calculations with index notation • Tensors/Transformation rule under a change of basis

Other projects

  • Introductory definitions is a short and simple introduction to linear algebra. The best part is the three links to three Youtube videos:
  1. Element-wise Matrix Operations
  2. Matrix multiplication
  3. Gaussian Elimination

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See also

  1. Wikipedia: Linear algebra